Flat Belt Drives n 677 * Rope drives are discussed in Chapter 20. Flat Belt Drives 677 18 C H A P T E R 1. Introduction. 2. Selection of a Belt Drive. 3. Types of Belt Drives. 4. Types of Belts. 5. Material used for Belts. 6. Working Stresses in Belts. 7. Density of Belt Materials. 8. Belt Speed. 9. Coefficient of Friction Between Belt and Pulley 10. Standard Belt Thicknesses and Widths. 11. Belt Joints. 12. Types of Flat Belt Drives. 13. Velocity Ratio of a Belt Drive. 14. Slip of the Belt. 15. Creep of Belt. 16. Length of an Open Belt Drive. 17. Length of a Cross Belt Drive. 18. Power transmitted by a Belt. 19. Ratio of Driving Tensions for Flat Belt Drive. 20. Centrifugal Tension. 21. Maximum Tension in the Belt. 22. Condition for Transmission of Maximum Power. 23. Initial Tension in the Belt. 18.118.1 18.118.1 18.1 IntrIntr IntrIntr Intr oductionoduction oductionoduction oduction The belts or *ropes are used to transmit power from one shaft to another by means of pulleys which rotate at the same speed or at different speeds. The amount of power transmitted depends upon the following factors : 1. The velocity of the belt. 2. The tension under which the belt is placed on the pulleys. 3. The arc of contact between the belt and the smaller pulley. 4. The conditions under which the belt is used. It may be noted that (a) The shafts should be properly in line to insure uniform tension across the belt section. (b) The pulleys should not be too close together, in order that the arc of contact on the smaller pulley may be as large as possible. CONTENTS CONTENTS CONTENTS CONTENTS 678 n A Textbook of Machine Design (c) The pulleys should not be so far apart as to cause the belt to weigh heavily on the shafts, thus increasing the friction load on the bearings. (d) A long belt tends to swing from side to side, causing the belt to run out of the pulleys, which in turn develops crooked spots in the belt. (e) The tight side of the belt should be at the bottom, so that whatever sag is present on the loose side will increase the arc of contact at the pulleys. ( f ) In order to obtain good results with flat belts, the maximum distance between the shafts should not exceed 10 metres and the minimum should not be less than 3.5 times the diameter of the larger pulley. 18.218.2 18.218.2 18.2 Selection of a Belt DriveSelection of a Belt Drive Selection of a Belt DriveSelection of a Belt Drive Selection of a Belt Drive Following are the various important factors upon which the selection of a belt drive depends: 1. Speed of the driving and driven shafts, 2. Speed reduction ratio, 3. Power to be transmitted, 4. Centre distance between the shafts, 5. Positive drive requirements, 6. Shafts layout, 7. Space available, and 8. Service conditions. 18.318.3 18.318.3 18.3 TT TT T ypes of Belt Drypes of Belt Dr ypes of Belt Drypes of Belt Dr ypes of Belt Dr iviv iviv iv eses eses es The belt drives are usually classified into the following three groups: 1. Light drives. These are used to transmit small powers at belt speeds upto about 10 m/s as in agricultural machines and small machine tools. 2. Medium drives. These are used to transmit medium powers at belt speeds over 10 m/s but up to 22 m/s, as in machine tools. 3. Heavy drives. These are used to transmit large powers at belt speeds above 22 m/s as in compressors and generators. 18.418.4 18.418.4 18.4 TT TT T ypes of Beltsypes of Belts ypes of Beltsypes of Belts ypes of Belts Though there are many types of belts used these days, yet the following are important from the subject point of view: 1. Flat belt. The flat as shown in Fig. 18.1 (a), is mostly used in the factories and workshops, where a moderate amount of power is to be transmitted, from one pulley to another when the two pulleys are not more than 8 metres apart. Flat belt V-belt Circular belt ( ) Flat belt.a ( ) V-belt.b ( ) Circular belt.c Fig. 18.1. Types of belts 2. V- belt. The V-belt as shown in Fig. 18.1 (b), is mostly used in the factories and workshops, where a great amount of power is to be transmitted, from one pulley to another, when the two pulleys are very near to each other. 3. Circular belt or rope. The circular belt or rope as shown in Fig. 18.1 (c) is mostly used in the factories and workshops, where a great amount of power is to be transmitted, from one pulley to another, when the two pulleys are more than 8 metres apart. Flat Belt Drives n 679 If a huge amount of power is to be transmitted, then a single belt may not be sufficient. In such a case, wide pulleys (for V-belts or circular belts) with a number of grooves are used. Then a belt in each groove is provided to transmit the required amount of power from one pulley to another. Note : The V-belt and rope drives are discussed in Chapter 20. 18.518.5 18.518.5 18.5 Material used for BeltsMaterial used for Belts Material used for BeltsMaterial used for Belts Material used for Belts The material used for belts and ropes must be strong, flexible, and durable. It must have a high coefficient of friction. The belts, according to the material used, are classified as follows: 1. Leather belts. The most important material for flat belt is leather. The best leather belts are made from 1.2 metres to 1.5 metres long strips cut from either side of the back bone of the top grade steer hides. The hair side of the leather is smoother and harder than the flesh side, but the flesh side is stronger. The fibres on the hair side are perpendicular to the surface, while those on the flesh side are interwoven and parallel to the surface. Therefore for these reasons the hair side of a belt should be in contact with the pulley surface as shown in Fig. 18.2. This gives a more intimate contact between belt and pulley and places the greatest tensile strength of the belt section on the outside, where the tension is maximum as the belt passes over the pulley. The leather may be either oak-tanned or mineral salt-tanned e.g. chrome-tanned. In order to increase the thickness of belt, the strips are cemented together. The belts are specified according to the number of layers e.g. single, double or triple ply and according to the thickness of hides used e.g. light, medium or heavy. ( ) Single layer belt.a ( ) Double layer belt.b Direction of motion Direction of motion Hair side Hair side Fig. 18.2. Leather belts. The leather belts must be periodically cleaned and dressed or treated with a compound or dressing containing neats foot or other suitable oils so that the belt will remain soft and flexible. 2. Cotton or fabric belts. Most of the fabric belts are made by folding convass or cotton duck to three or more layers (depending upon the thickness desired) and stitching together. These belts are woven also into a strip of the desired width and thickness. They are impregnated with some filler like linseed oil in order to make the belt water-proof and to prevent injury to the fibres. The cotton belts are cheaper and suitable in warm climates, in damp atmospheres and in exposed positions. Since the cotton belts require little attention, therefore these belts are mostly used in farm machinery, belt conveyor etc. 3. Rubber belt. The rubber belts are made of layers of fabric impregnated with rubber composition and have a thin layer of rubber on the faces. These belts are very flexible but are quickly destroyed if allowed to come into contact with heat, oil or grease. One of the principle advantage of these belts is that they may be easily made endless. These belts are found suitable for saw mills, paper mills where they are exposed to moisture. 4. Balata belts. These belts are similar to rubber belts except that balata gum is used in place of rubber. These belts are acid proof and water proof and it is not effected by animal oils or alkalies. The balata belts should not be at temperatures above 40°C because at this temperature the balata begins to soften and becomes sticky. The strength of balata belts is 25 per cent higher than rubber belts. 680 n A Textbook of Machine Design 18.618.6 18.618.6 18.6 WW WW W oror oror or king Strking Str king Strking Str king Str esses in Beltsesses in Belts esses in Beltsesses in Belts esses in Belts The ultimate strength of leather belt varies from 21 to 35 MPa and a factor of safety may be taken as 8 to 10. However, the wear life of a belt is more important than actual strength. It has been shown by experience that under average conditions an allowable stress of 2.8 MPa or less will give a reasonable belt life. An allowable stress of 1.75 MPa may be expected to give a belt life of about 15 years. 18.718.7 18.718.7 18.7 Density of Belt MaterialsDensity of Belt Materials Density of Belt MaterialsDensity of Belt Materials Density of Belt Materials The density of various belt materials are given in the following table. TT TT T aa aa a ble 18.1.ble 18.1. ble 18.1.ble 18.1. ble 18.1. Density of belt ma Density of belt ma Density of belt ma Density of belt ma Density of belt ma terter terter ter ialsials ialsials ials . Material of belt Mass density in kg / m 3 Leather 1000 Convass 1220 Rubber 1140 Balata 1110 Single woven belt 1170 Double woven belt 1250 18.818.8 18.818.8 18.8 Belt SpeedBelt Speed Belt SpeedBelt Speed Belt Speed A little consideration will show that when the speed of belt increases, the centrifugal force also increases which tries to pull the belt away from the pulley. This will result in the decrease of power transmitted by the belt. It has been found that for the efficient transmission of power, the belt speed 20 m/s to 22.5 m/s may be used. 18.918.9 18.918.9 18.9 CoefCoef CoefCoef Coef ff ff f icient of Fricient of Fr icient of Fricient of Fr icient of Fr iction Betwiction Betw iction Betwiction Betw iction Betw een Belt and Pulleeen Belt and Pulle een Belt and Pulleeen Belt and Pulle een Belt and Pulle yy yy y The coefficient of friction between the belt and the pulley depends upon the following factors: 1. The material of belt; 2. The material of pulley; 3. The slip of belt; and 4. The speed of belt. According to C.G. Barth, the coefficient of friction (!) for oak tanned leather belts on cast iron pulley, at the point of slipping, is given by the following relation, i.e. ∀∀∀∀∀∀∀∀∀∀! = 42.6 0.54 – 152.6 v # where v = Speed of the belt in metres per minute. The following table shows the values of coefficient of friction for various materials of belt and pulley. Belts used to drive wheels Flat Belt Drives n 681 TT TT T aa aa a ble 18.2.ble 18.2. ble 18.2.ble 18.2. ble 18.2. Coef Coef Coef Coef Coef ff ff f icient of fricient of fr icient of fricient of fr icient of fr iction betwiction betw iction betwiction betw iction betw een belt and pulleeen belt and pulle een belt and pulleeen belt and pulle een belt and pulle yy yy y . Pulley material Belt material Cast iron, steel Wood Compressed Leather Rubber Dry Wet Greasy paper face face 1. Leather oak tanned 0.25 0.2 0.15 0.3 0.33 0.38 0.40 2. Leather chrome tanned 0.35 0.32 0.22 0.4 0.45 0.48 0.50 3. Convass-stitched 0.20 0.15 0.12 0.23 0.25 0.27 0.30 4. Cotton woven 0.22 0.15 0.12 0.25 0.28 0.27 0.30 5. Rubber 0.30 0.18 — 0.32 0.35 0.40 0.42 6. Balata 0.32 0.20 — 0.35 0.38 0.40 0.42 18.10 Standar18.10 Standar 18.10 Standar18.10 Standar 18.10 Standar d Belt d Belt d Belt d Belt d Belt ThicThic ThicThic Thic knesses and knesses and knesses and knesses and knesses and WW WW W idthsidths idthsidths idths The standard flat belt thicknesses are 5, 6.5, 8, 10 and 12 mm. The preferred values of thicknesses are as follows: (a) 5 mm for nominal belt widths of 35 to 63 mm, (b) 6.5 mm for nominal belt widths of 50 to 140 mm, (c) 8 mm for nominal belt widths of 90 to 224 mm, (d) 10 mm for nominal belt widths of 125 to 400 mm, and (e) 12 mm for nominal belt widths of 250 to 600 mm. The standard values of nominal belt widths are in R10 series, starting from 25 mm upto 63 mm and in R 20 series starting from 71 mm up to 600 mm. Thus, the standard widths will be 25, 32, 40, 50, 63, 71, 80, 90, 100, 112, 125, 140, 160, 180, 200, 224, 250, 280, 315, 355, 400, 450, 500, 560 and 600 mm. 18.11 Belt Joints18.11 Belt Joints 18.11 Belt Joints18.11 Belt Joints 18.11 Belt Joints When the endless belts are not available, then the belts are cut from big rolls and the ends are joined together by fasteners. The various types of joints are 1. Cemented joint, 2. Laced joint, and 3. Hinged joint. The cemented joint, as shown in Fig. 18.3 (a), made by the manufacturer to form an endless belt, is preferred than other joints. The laced joint is formed by punching holes in line across the belt, leaving a margin between the edge and the holes. A raw hide strip is used for lacing the two ends together to form a joint. This type of joint is known as straight-stitch raw hide laced joint, as shown in Fig. 18.3 (b). Metal laced joint as shown in Fig. 18.3 (c), is made like a staple connection. The points are driven through the flesh side of the belt and clinched on the inside. Sometimes, metal hinges may be fastened to the belt ends and connected by a steel or fibre pin as shown in Fig. 18.3 (d). 682 n A Textbook of Machine Design ( ) Comented joint.a ( ) Metal laced joint.c ( ) Hinged joint.d ( ) Straight-stitch raw hide laced joint.b Hair side Flesh side Ready to drive in Finished joint Disjointed Jointed Fig. 18.3. Belt joints. The following table shows the efficiencies of these joints. TT TT T aa aa a ble 18.3.ble 18.3. ble 18.3.ble 18.3. ble 18.3. Ef Ef Ef Ef Ef ff ff f iciencies of belt jointsiciencies of belt joints iciencies of belt jointsiciencies of belt joints iciencies of belt joints . Type of joint Efficiency (%) Type of joint Efficiency (%) 1. Cemented, endless, 90 to 100 4. Wire laced by hand 70 to 80 cemented at factory 2. Cemented in shop 80 to 90 5. Raw-hide laced 60 to 70 3. Wire laced by machine 75 to 85 6. Metal belt hooks 35 to 40 18.1218.12 18.1218.12 18.12 TT TT T ypes of Flaypes of Fla ypes of Flaypes of Fla ypes of Fla t Belt Drt Belt Dr t Belt Drt Belt Dr t Belt Dr iviv iviv iv eses eses es The power from one pulley to another may be transmitted by any of the following types of belt drives. Cross or twist belt drive Flat Belt Drives n 683 1. Open belt drive. The open belt drive, as shown in Fig. 18.4, is used with shafts arranged parallel and rotating in the same direction. In this case, the driver A pulls the belt from one side (i.e. lower side RQ) and delivers it to the other side (i.e. upper side LM). Thus the tension in the lower side belt will be more than that in the upper side belt. The lower side belt (because of more tension) is known as tight side whereas the upper side belt (because of less tension) is known as slack side, as shown in Fig. 18.4. Fig. 18.4. Open belt drive. 2. Crossed or twist belt drive. The crossed or twist belt drive, as shown in Fig. 18.5, is used with shafts arranged parallel and rotating in the opposite directions. In this case, the driver pulls the belt from one side (i.e. RQ) and delivers it to the other side (i.e. LM). Thus, the tension in the belt RQ will be more than that in the belt LM. The belt RQ (because of more tension) is known as tight side, whereas the belt LM (because of less tension) is known as slack side, as shown in Fig. 18.5. A little consideration will show that at a point where the belt crosses, it rubs against each other and there will be excessive wear and tear. In order to avoid this, the shafts should be placed at a Fig. 18.5. Crossed or twist belt drive. 684 n A Textbook of Machine Design maximum distance of 20 b, where b is the width of belt and the speed of the belt should be less than 15 m/s. 3. Quarter turn belt drive. The quarter turn belt drive (also known as right angle belt drive) as shown in Fig. 18.6 (a), is used with shafts arranged at right angles and rotating in one definite direction. In order to prevent the belt from leaving the pulley, the width of the face of the pulley should be greater or equal to 1.4 b, where b is width of belt. In case the pulleys cannot be arranged as shown in Fig. 18.6 (a) or when the reversible motion is desired, then a quarter turn belt drive with a guide pulley, as shown in Fig. 18.6 (b), may be used. Driver Driven Guide pulley (a) Quarter turn belt drive. (b) Quarter turn belt drive with guide pulley. Fig. 18.6 4. Belt drive with idler pulleys. A belt drive with an idler pulley (also known as jockey pulley drive) as shown in Fig. 18.7, is used with shafts arranged parallel and when an open belt drive can not be used due to small angle of contact on the smaller pulley. This type of drive is provided to obtain high velocity ratio and when the required belt tension can not be obtained by other means. Fig. 18.7. Belt drive with single idler pulley. Fig. 18.8. Belt drive with many idler pulleys. When it is desired to transmit motion from one shaft to several shafts, all arranged in parallel, a belt drive with many idler pulleys, as shown in Fig. 18.8, may be employed. 5. Compound belt drive. A compound belt drive as shown in Fig. 18.9, is used when power is transmitted from one shaft to another through a number of pulleys. Flat Belt Drives n 685 Fig. 18.9. Compound belt drive. 6. Stepped or cone pulley drive. A stepped or cone pulley drive, as shown in Fig. 18.10, is used for changing the speed of the driven shaft while the main or driving shaft runs at constant speed. This is accomplished by shifting the belt from one part of the steps to the other. Cone pulley Driven shaft Main or driving shaft Driving pulley Line shaft Loose pulley Fast pulley Machine shaft Fig. 18.10. Stepped or cone pulley drive. Fig. 18.11. Fast and loose pulley drive. 7. Fast and loose pulley drive. A fast and loose pulley drive, as shown in Fig. 18.11, is used when the driven or machine shaft is to be started or stopped whenever desired without interferring with the driving shaft. A pulley which is keyed to the machine shaft is called fast pulley and runs at the same speed as that of machine shaft. A loose pulley runs freely over the machine shaft and is incapable of transmitting any power. When the driven shaft is required to be stopped, the belt is pushed on to the loose pulley by means of sliding bar having belt forks. 686 n A Textbook of Machine Design 18.13 18.13 18.13 18.13 18.13 VV VV V elocity Raelocity Ra elocity Raelocity Ra elocity Ra tio of a Belt Drtio of a Belt Dr tio of a Belt Drtio of a Belt Dr tio of a Belt Dr iviv iviv iv ee ee e It is the ratio between the velocities of the driver and the follower or driven. It may be expressed, mathematically, as discussed below: Let d 1 = Diameter of the driver, d 2 = Diameter of the follower, N 1 = Speed of the driver in r.p.m., N 2 = Speed of the follower in r.p.m., ∃ Length of the belt that passes over the driver, in one minute = %∀d 1 N 1 Similarly, length of the belt that passes over the follower, in one minute = %∀d 2 N 2 Since the length of belt that passes over the driver in one minute is equal to the length of belt that passes over the follower in one minute, therefore ∵ %∀d 1 N 1 = %∀d 2 N 2 and velocity ratio, 21 12 Nd Nd & When thickness of the belt (t) is considered, then velocity ratio, = 21 12 Ndt Ndt # & # Notes : 1. The velocity ratio of a belt drive may also be obtained as discussed below: We know that the peripheral velocity of the belt on the driving pulley, ∋ 1 = 11 m/s 60 dN% and peripheral velocity of the belt on the driven pulley, ∋ 2 = 22 m/s 60 dN% When there is no slip, then ∋ 1 = ∋ 2 . ∃ 11 2 2 2 1 12 or 60 60 dN dN N d Nd %% && 2. In case of a compound belt drive as shown in Fig. 18.7, the velocity ratio is given by 413 124 Ndd Ndd ( & ( or Speed of last driven Product of diameters of drivers = Speed of first driver Product of diameters of drivens 18.14 Slip of the Belt18.14 Slip of the Belt 18.14 Slip of the Belt18.14 Slip of the Belt 18.14 Slip of the Belt In the previous articles we have discussed the motion of belts and pulleys assuming a firm frictional grip between the belts and the pulleys. But sometimes, the frictional grip becomes insufficient. This may cause some forward motion of the driver without carrying the belt with it. This is called slip of the belt and is generally expressed as a percentage. The result of the belt slipping is to reduce the velocity ratio of the system. As the slipping of the belt is a common phenomenon, thus the belt should never be used where a definite velocity ratio is of importance (as in the case of hour, minute and second arms in a watch). Let s 1 % = Slip between the driver and the belt, and s 2 % = Slip between the belt and follower, [...]... side of the belt, and T2 = Tension in the slack side of the belt We have discussed in Art 18.19 (Note 2) that when the pulleys are made of different material [i.e when the pulleys have different coefficient of friction (!) or different angle of contact (7)], then the design will be refer to a pulley for which !.7 is small Since the ratio of tensions will be constant, i.e 710 n A Textbook of Machine Design. .. tension in it, shall not exceed 15 N/mm of width for a belt of 10 mm thickness This rule is applied to determine width of belt required to transmit 37 kW, under the following conditions : Angle of lap = 165°; Coefficient of friction = 0.3; Velocity of belt = 1500 m/min; Density of leather = 950 kg/m3 712 n A Textbook of Machine Design Find the width of belt required Assuming limiting friction between belt... of the belt subtending an angle d7 at the centre of the pulley, as shown in Fig 18.18 dq 2 P dq Q dq 2 TC Fig 18.18 Centrifugal tension 696 n A Textbook of Machine Design Let m = Mass of belt per unit length in kg, v = Linear velocity of belt in m/s, r = Radius of pulley over which the belt runs in metres, and TC = Centrifugal tension acting tangentially at P and Q in newtons We know that length of. .. 1272 mm We know that length of belt, (d – d 2 )2 % ( d1 # d 2 ) # 2 x # 1 L = 2 4x (218 – 636)2 % = (218 # 636) # 2 ( 1272 # 2 4 ( 1272 = 1342 + 2544 + 34 = 3920 mm = 3.92 m Ans 708 n A Textbook of Machine Design 3 Cross-sectional area of the belt Let a = Cross-sectional area of the belt First of all, let us find the angle of contact for both the pulleys From the geometry of the figure, we find that... value of 6 = x (r1 # r2 ) (r # r2 )2 (r1 # r2 ) # 2 x – 1 L = % (r1 # r2) # 2 ( x x 2 2 2 (r1 # r2) (r # r 2 ) # 2x – 1 = % (r1 # r2 ) # x x 692 n A Textbook of Machine Design (r1 # r2 )2 (in terms of pulley radii) x 2 (d # d 2 ) % (d1 # d 2 ) # 2 x # 1 = (in terms of pulley diameters) 2 4x It may be noted that the above expression is a function of (r1 + r2) It is thus obvious, that if sum of the... engine shaft is of 2 m diameter and that of the machine shaft is 1 m diameter If the belt thickness is 5 mm; determine the speed of the machine shaft, when 1 there is no slip; and 2 there is a slip of 3% [Ans 239.4 r.p.m ; 232.3 r.p.m.] 2 A pulley is driven by a flat belt running at a speed of 600 m/min The coefficient of friction between the pulley and the belt is 0.3 and the angle of lap is 160° If... r2) + 2 × 690 n A Textbook of Machine Design (r1 – r2 )2 x (d – d 2 )2 % (d1 # d 2 ) # 2 x # 1 = 2 4x = % (r1 + r2) + 2x + (in terms of pulley radii) (in terms of pulley diameters) Driv ive Cross 18.17 Length of a Cross Belt Drive We have discussed in Art 18.12 that in a cross belt drive, both the pulleys rotate in the opposite directions as shown in Fig 18.14 Let r1 and r2 = Radii of the larger and... 450 mm ; d 3 = 900 mm ; d4 = 150 mm ; s1 = s2 = 2% The arrangement of belt drive is shown in Fig 18.12 688 n A Textbook of Machine Design Let 1 When there is no slip We know that ∃ N4 = Speed of the dynamo shaft d1 ( d3 750 ( 900 N4 N or 4 & & 10 = 150 450 ( 150 N1 d2 ( d4 N4 = 150 × 10 = 1500 r.p.m Ans Fig 18.12 2 When there is a slip of 2% at each drive We know that d1 ( d3 ) s1 ∗ ) s2 ∗ N4 = +1 –... )T ∗ & 0.3756 or 1 & 2.375 log + 1 , = 2.3 T2 − T2 From equations (i) and (ii), we find that T1 = 2199 N ; and T2 = 926 N .(ii) (Taking antilog of 0.3756) 700 n A Textbook of Machine Design Let b = Width of the belt required in metres We know that mass of the belt per metre length, m = Area × length × density = b × t × l × ; = b × 0.0095 × 1 × 1100 = 10.45 b kg/m and centrifugal tension, TC = m.v2... MPa = 2.1 × 106 N/m2 ; ; = 1000 kg/m3 ; 7 = 165° = 165 × %/180 = 2.88 rad ; ! = 0.3 Let T1 = Tension in the tight side of the belt, and T2 = Tension in the slack side of the belt We know that velocity of the belt, % d N % ( 0.2 ( 2250 & & 23.6 m/s v = 60 60 702 n A Textbook of Machine Design and power transmitted (P), 20 × 103 = (T1 – T2) v. . drive. 684 n A Textbook of Machine Design maximum distance of 20 b, where b is the width of belt and the speed of the belt should be less than 15. diameters of drivers = Speed of first driver Product of diameters of drivens 18.14 Slip of the Belt18.14 Slip of the Belt 18.14 Slip of the Belt18.14 Slip of